Question: In this system, virtual addresses are 52 bits long, and physical addresses are 40 bits long. (a) What is the smallest page size that will

In this system, virtual addresses are 52 bits long, and physical addresses are 40 bits long.

(a) What is the smallest page size that will still allow a PTE to fit into a 4 byte word? HINT: remember that the PTE only needs to store the physical frame number, not a full address.

(b) How big (number of entries) would a single level page table for this system be? From this point onward, assume 8 KB pages.

(c) From Problem 2b, its clear that we need multi-level page tables. If each top-level entry covered 1 GB, how big would the top-level table be? How many entries would be in each second-level page table?

(d) Instead, we use a three-level page table where top-level entries each refer to 256 GB and a level 2 page table has 8192 entries. How much memory does a single entry in each of the three levels map, and how many entries are in a page table in each of the three levels? (Yes, the answers to some of these values are already provided as part of the question.)

(e) AssumeaprogramusingthepagingsysteminProblem2dhasthreevalidregions:0x10000x8fffffff, 0xf000000000x1000007fff, and 0xfff90000000000xfffffffffffff. How much space (in KB) is required for the page tables for this program? Assume that a page table in a given level may not be truncatedif you need part of a particular page table, you need space for all of it.

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